Let $$m$$ be a positive integer, and let $$a_0, a_1,\ldots,a_m$$ be a sequence of integers such that $$a_0 = 37, a_1 = 72, a_m = 0,$$ and $$a_{k+1} = a_{k-1} - \frac 3{a_k}$$ for $$k = 1,2,\ldots, m-1.$$ Find $$m.$$

(第二十三届AIME2 2005 第11题)